Problem: Express this quotient in scientific notation: ${\frac{1.300\times 10^{2}} {2.0\times 10^{5}}}$
Solution: Start by collecting like terms together. $= {\frac{1.300} {2.0}} \times{\frac{10^{2}} {10^{5}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.65 \times 10^{2\,-\,5}$ $= 0.65 \times 10^{-3}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.65$ is the same as $6.50 \div 10$ , or $6.50 \times 10^{-1}$ $ = {6.50 \times 10^{-1}} \times 10^{-3} $ $= 6.50\times 10^{-4}$